We show that (in the description by rate equations) a laser with convention
al optical feedback has the symmetry of any rotation of the electric field,
whereas a laser with phase-conjugate feedback has the symmetry of only the
rotations of the electric field over 0 and pi. This has important conseque
nces for dynamics and bifurcations of these two laser systems. Most importa
ntly, a PCF laser shows symmetry breaking and restoring bifurcations, somet
hing that does not occur in a COF laser. (C) 2000 Elsevier Science B.V. All
rights reserved.